Current widely accepted understanding of the origin of motion is based on the Newtonian, Special (SR), and General Relativity (GR) theories wherein an external force or agency is required to impart motion to a classical mass. Similarly, quantum theories assume a preexisting field or quantum fluctuations (wave-functions) as a fundamental reality. Maxwell’s theory also assumes a photon having an inherent speed the speed of light and zero mass at its birth and throughout its lifetime. Part-1 of this paper describes the missing physics of the origin of motion based on the well-established principle of mass-energy equivalence that requires a nonzero rest mass for originating nonzero kinetic energy or motion. The proposed Universal Relativity Model (URM) based on special relativity theory describes a universal model predicting classical as well as quantum behaviors of both massive and massless particles in a single model that is shown to remove prevailing deficiencies/inconsistencies and paradoxes of the current widely accepted physics and cosmology theories. The proposed model describes a spontaneous (no external force or agency required) relativistic mass creation/dilation process allowing a nonzero photon mass at rest (emission and absorption), which dilates to zero as it expands and accelerates to the speed of light through uninterrupted space. The model thus bridges gaps between relativity and Maxwell’s theories. Integrating gravity into the model leads to a fundamental universe model that is shown to predict the observed universe/galaxy behavior and resolves paradoxes of the big bang cosmology including dark energy, dark matter, cosmological constant, and big bang (GR) singularity without the need for superluminous inflation. The model also makes testable predictions for falsification via future observations and provides a new fundamental understanding of universal constants such as c, commonly known as the speed of light. The results may have significant implications for the current standard model, big bang cosmology, and fundamental understanding of the universe. Part-2 of the paper extends the relativistic model to describe the physics of the observed spontaneous complementary or dualistic wave-particle behavior of quantum particles as an alternative to the well-known de Broglie model. It explains the inner workings of quantum mechanics resolving its major paradoxes including the collapse of the wave function, parallel universes, vacuum energy, and nonlocality (spooky action-at-distance).